If A = [(1,0)(-1,7)] and B = [(0,4)(-1,7)] , find (3A^2 – 2B + I).

Question

If A = \( \begin{bmatrix} 1 & 0 \\[0.3em] -1 & 7 \\[0.3em] \end{bmatrix}\) and B = \( \begin{bmatrix} 0& 4 \\[0.3em] -1 & 7 \\[0.3em] \end{bmatrix},\) find (3A² – 2B + I).

A = [(1,0)(-1,7)]

B = [(0,4)(-1,7)]

Answer 1

Given : A = \( \begin{bmatrix} 1& 0 \\[0.3em] -1 & 7 \\[0.3em] \end{bmatrix}\) and B = \( \begin{bmatrix} 0& 4 \\[0.3em] -1 & 7 \\[0.3em] \end{bmatrix},\)

Matrices A and B are of order 2 x 2.

To find : (3A² – 2B + I).

Formula used :

Where c_ij = a_i1b_1j + a_i2b_2j + a_i3b_3j + ……………… + a_inb_nj

A² is a matrix of order 2 x 2.

3A² – 2B + I

3A² – 2B + I = \( \begin{bmatrix} 4&-8 \\[0.3em] -22 &134 \\[0.3em] \end{bmatrix}\)